In the arrangement shown in fig, pulleys D and E are small and frictionless. They do not rotate byt threads slip over then without friction and their masses being 4kg and 11.25 kg, respectively. While the masses of blocks A,B, and C, are `2m, m and m'`,respectively. when the system is released from rest, downward accelerations of blocks B and C relative to A are found to be `5ms^(-2) and 3ms^(-2)`, respectively. Calculate:
a. Acceleration of blocks B and C, relative to the ground.
b. Mass of each block `(g=10ms^(-2))`

Options

A. `2 ms^(-2)` downwards
B. `1 ms^(-2)` upwards
C. `3 ms^(-2)` upwards
D. `1.5 ms^(-2)` downwards

Answer

B

Explanation

Acceleration of dirrerent objects is shown in figure. All the acceleration are w.r.t. ground
Given : `a_(3)=a_(4)` ..(i)
`a_(2)+a_(1)=1` ..(ii)
`a_(3)+a_(1)=5` ..(iii)
from fig, we can write
`-a_(5)=(a_(2)+a_(3))/(2) ..(iv)`
`a_(1)=(a_(4)+a_(5))/(2)` ..(v)
Solving the above equations, we get
`a_(1)=2 ms^(-2), a_(2) = 1ms^(-2)`,
`a_(3)=a_(4)=3 ms^(-2)`.